Categorical logic in models of concurrency by Purandar Bhaduri Download PDF EPUB FB2
Cite this paper as: Winskel G. () Categories of models for concurrency. In: Brookes S.D., Roscoe A.W., Winskel G. (eds) Seminar on by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This is a report on a mathematician's effort to understand some concurrency theory.
The starting point is a logical interpretation of Nielsen and Winskel's  account of the basic models of concurrency. Upon the obtained logical structures, we build a calculus of relations which yields, when cut down by. Like your usual North-Holland text, this is a book in *pure logic*: the "topos" (discovered by F.
William Lawvere in the '60s) is the category which has the structure necessary to model quantificational logic, and Goldblatt's goal is to make the discoveries of Lawvere and others in this area available to people with a standard training in Cited by: J.
Meseguer, Conditional Rewriting Logic as a Unified Model of Concurrency, in Selected Papers of 2 th Workshop on Concurrency and Compositionality, Theoretical Computer Sciepp.
73– CrossRef Google ScholarCited by: Recently, Joyal, Nielsen and Winskel suggested a categorical definition of bisimulation, applicable to a wide range of models in con-currency with an accompanying notion of observations.
The definition is in terms of span of open maps, and it coincides with Park and Milner’s strong bisimulation for the standard model of labelled transition Cited by: Models of concurrency, categories, and games Description.
Mathematical models of concurrent or distributed systems typically belong to one of two families: interleaving models, which represent a concurrent system by enumerating its exponentially many schedulings, and independence models, which instead represent explicitly information of causality or independence between computational events.
model of concurrency, and linear logic [Gir86]. Each of the Parts II, III and IV of the thesis describes a correspondence between linear logic and Petri nets: each approach could be developed further to give a linear specification language for Petri nets, thus addressing a central problem in the theory of concurrent programming languages.
This book provides a gentle, software engineering oriented introduction to category theory. Assuming only a minimum of mathematical preparation, this book explores the use of categorical constructions from the point of view of the methods and techniques that have been proposed for the engineering of complex software systems: object-oriented development, software architectures, logical and.
This book constitutes the proceedings of the 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETSwhich was supposed to be held in Paris, France, in June The conference was held virtually due to the COVID pandemic.
Categorical models of linear logic revisited Paul-Andr´e Melli`es CNRS, Universit´e Paris 7 Abstract In this survey, we review the existing categorical axiomatizations of linear logic, with a special emphasis on Seely and Lafont presentations. In a ﬁrst part, we explain why.
A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of l. Purchase Categorical Logic and Type Theory, Volume - 1st Edition. Print Book & E-Book. ISBNThis book combines coalgebraic reasoning, stochastic systems and logics.
It provides an insight into the principles of coalgebraic logic from a categorical point of view, and applies these systems to interpretations of stochastic coalgebraic logics, which include well-known modal logics and continuous time branching logics.
The chapter begins with an introduction describing the development of categorical logic from the s. The next section, `Categories and Deductive Systems’, describes the relationship between categories and propositional logic, while the ensuing section, `Functorial Semantics’, is devoted to Lawvere’s provision of the first-order theory of models with a categorical formulation.
His current research interests are the semantics of concurrency, process description languages, constraint programming, graph transformation systems, coordination models, algebraic and categorical models of concurrency, models and languages for open distributed systems, network-aware programming, service-oriented computing, and collective.
logic (including modal and categorical logic) (higher) category theory; formal models of computer security; concurrency and process calculi; Publications.
Kavvos (). “Dual-Context Calculi for Modal Logic”. In: Logical Methods in Computer Science 16 (3). Daniel Gratzer, G. Kavvos, Andreas Nuyts, Lars Birkedal. A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation.
linear logic and their applications to concurrency-of recent work on the applications of linear logic to concurrency, with special emphasis on Petri nets and on the use of categorical models. In particular, it presents a synthesis of all the previous work on this project by Marti-Oliet and. His current research interests are the semantics of concurrency, process description languages, constraint programming, graph transformation systems, coordination models, algebraic and categorical models of concurrency, models and languages for open distributed systems, network-aware programming, service-oriented computing, and collective Author: Roberto Bruni, Ugo Montanari.
One nice form of concurrency, called “event-loop concurrency”, models concurrency with a bunch of “vats”, each of which consists of a lambda term and a queue of messages. On each “turn”, the vat pops the top message off the queue and applies the lambda term to.
Models of Sharing Graphs presents a sound mathematical basis for reasoning about models of computation involving shared resources, including graph rewriting systems, denotational semantics and concurrency theory.
An algebraic approach, based on the language of category theory, is taken. Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics - Ebook written by Silvio Ghilardi, M.
Zawadowski. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical. This can be viewed as a first step towards representing fairness in categorical models for concurrency.
The open map bisimulation is shown to coincide with extended bisimulation of Hennessy and Stirling, which is essentially fair CTL ∗-bisimulation. Sheaf semantics for concurrent interacting objects - Volume 2 Issue 2 - Joseph A. Goguen. Bistructures form a categorical model of Girard's classical linear logic in which the involution of linear logic is modelled, roughly speaking, by a reversal of the roles of input and output.
Categorical semantics Categorical logic introduces the notion of structure valued in a category C with the classical model theoretic notion of a structure appearing in the particular case where C is the category of sets and functions.
This notion has proven useful when the set-theoretic notion of a model lacks generality and/or is inconvenient. These 5 isolation levels work on two major concurrency models: Pessimistic model - In the pessimistic model of managing concurrent data access, the readers can block writers, and the writers can.
We give a taste of categorical logic and present selected examples. The choice of examples is guided by the wish to prepare the reader for understanding current research papers on step-indexed models for modular reasoning about concurrent higher-order imperative programming languages.
Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics (Trends in Logic Book 14) - Kindle edition by Ghilardi, Silvio, Zawadowski, M., Zawadowski, Marek.
Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Sheaves, Games, and Model Manufacturer: Springer Netherlands.
The paper shows how the Scott–Koymans theorem for the untyped λ-calculus can be extended to the differential main result is that every model of the untyped differential λ-calculus may be viewed as a differential reflexive object in a Cartesian-closed differential extension of the Scott–Koymans theorem depends critically on unraveling the somewhat subtle.
This book provides a gentle, software engineering oriented introduction to category theory. Assuming only a minimum of mathematical preparation, this book explores the use of categorical constructions from the point of view of the methods and techniques that have been proposed for the engineering of complex software systems: object-oriented development, software architectures, logical and Reviews: 4.Bunched logic is a variety of substructural logic proposed by Peter O'Hearn and David d logic provides primitives for reasoning about resource composition, which aid in the compositional analysis of computer and other has category-theoretic and truth-functional semantics which can be understood in terms of an abstract concept of resource, and a proof theory in which the.The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics.